A charged particle of mass $m = 2\ kg$ and charge $1μC$ is projected from a horizontal ground at an angle $\theta = 45^o$ with speed $10\ ms^{-1}$ . In space, a horizontal electric field towards the direction of projection $E = 2 \times 10^7\ NC^{-1}$ exists. The range of the projectile is......$m$
$20$
$60$
$200$
$180$
A particle of mass $\mathrm{m}$ and charge $\mathrm{q}$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)
The electric field inside a spherical shell of uniform surface charge density is
A stream of a positively charged particles having $\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }$ and velocity $\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s$ is deflected by an electric field $1.8 \hat{ j } kV / m$. The electric field exists in a region of $10 cm$ along $x$ direction. Due to the electric field, the deflection of the charge particles in the $y$ direction is $...........mm$
Two identical positive charges are fixed on the $y$ -axis, at equal distances from the origin $O$. A particle with a negative charge starts on the $x$ -axis at a large distance from $O$, moves along the $+ x$ -axis, passes through $O$ and moves far away from $O$. Its acceleration $a$ is taken as positive in the positive $x$ -direction. The particle’s acceleration a is plotted against its $x$ -coordinate. Which of the following best represents the plot?
The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $- q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement$(s)$ is(are)